So ill make a wild guess but im sure having big precints all around the world, having thousands of personnel and equiping them with state of the arc technology must cost at least a LOT.
So where are the funds coming? Goverment and/or private funding, companies under foundation control. Selling things ? A blood sacriface of fifty virgins related money printer?
From where??!!

As well as what Mcrfan343 said, I would imagine they have various interdimensional facilities to gain resources. An example of this is SCP-2400. After all, you could find entire universes made of materials the Foundation requires. It is also likely that the Foundation uses a form of cloning for getting personnel at times, a la SCP-2000.There also probably own other mining companies on Earth for resources.

I know it's much easier for the Foundation. What I post above was reference to X-Com since Chrom1312 mention it. If you ever play X-Com (at least the classic series), you would know that your main source of income is selling alien corpse and their artifacts, as well as producing and sell X-Com's original gears like laser cannon. Because the sponsor nations never pay enough. It's sort of joke, should have made it more clear, sorry.

The Foundation's situation will be more like X-Com's if they aren't THE top dog in supernatural world. Then threaten to leave the door open will likely to result in ORIA or the Insurgency taking over the sites than increasing fund.

But if you are playing enemy unknown when you try to sell the artifacts and corpses you realize you sold all of them the past week and the only thing to do is sit down in the corner and cry till end of the month and the 8th country leaves the council… im not saying that happened to me it did

It wouldnt be strange for the foundation to be internationally funded by (almost) all major goverments too. the foundation is also internationally authorised to work above juristiction soo…
And the foundation adresses safety problem that could affect everyone on the entire world and some even the universe… and its seems like the foundation is the only in the world or at least the one with the most experience, power and resources to do its job…

I personally believe that the Foundation is secretly funded by Marshal Carter and Dark. They are the ones that have the most to loose if the Foundation fails. Their entire bottom line relies on the sale of the anomalous; if the Foundation failed the anomalous would become normal and they would loose everything.

In my headcanon the Foundation started off as part of some government that split off to become their own group. All governments in the world would benefit greatly from the efforts of the Foundation. I therefore assume that at least most world powers and probably most countries fund the Foundation through their respective Department of Defence. Here's how I figure the phone conversation went:

Minister of Defence: 'So I read your proposal. I had no idea about the existence of your organization until two weeks ago when I was placed in this position, and now you're requesting funding?'

0-5: 'Yes.'

Minister of Defence: 'Why should we do that?'

0-5: 'Please read the instructions given to you by your predecessor.'

Minister of Defence: 'Oh yeah I read that alright! ''Protect us from anomalous hazards''? If this is some kind of scam to tap into government funding you'd better pray that we never find out. I can't believe people before me fell for this.'

0-5: 'So you will not continue funding? Without it we'll be unable to operate within your nation any longer. If that is your decision, we'll have to be forced to remove the Site and release any SCP's that are unable to be moved into the general public -'

Minister of Defence: 'Now hold on a minute! I didn't say that!'

0-5: 'So we have an agreement then?'

Minister of Defence: '…'

Minister of Defence: 'What in God's name are you keeping in there?'

0-5: 'Are you sure you wish to know?'

Minister of Defence: '…No. I don't. I'll forward the funding through my administration.'